Fractal character of crack propagation in epoxy and epoxy composites as revealed by photon emission during fracture
- PDF / 1,263,414 Bytes
- 13 Pages / 576 x 792 pts Page_size
- 101 Downloads / 220 Views
M. H. Engelhard and D. R. Baer Molecular Science Research Center, Pacific Northwest Laboratories, Richland, Washington 99352 (Received 6 April 1990; accepted 4 October 1990) We examine the photon emission accompanying rapid crack growth in an unfilled epoxy resin and in the same resin filled with alumina particles. The alumina particles substantially increase the toughness of the material and increase the photon emission intensities at least tenfold. We attribute the increased photon emission in the filled material to high densities of broken bonds near the alumina particles. The photon emission signals from both filled and unfilled materials show nonintegral (fractal) dimensions which are insensitive to the presence of the particles at the level of precision employed. Fractal dimension measurements of the fracture surfaces are likewise relatively insensitive to the presence of the filler, despite marked variations in apparent surface roughness. The photon emission signals were examined for the presence of chaos. Computations of the correlation exponent of Grassberger and Procaccia indicate that the photon emission fluctuations are not noise-like in character, and suggest deterministic chaos. Lyapunov exponent estimates on photon emission signals confirm the presence of chaotic processes. X-ray photoelectron spectroscopy and electron microscopy of the fracture surface indicate very little interfacial failure; i.e., fracture proceeds predominantly through the epoxy matrix in both filled and unfilled materials. Consequently, the character of the polymer matrix dominates the fracture process and therefore determines the fractal nature of the surface and the chaotic nature of the photon emission intensities in each material.
I. INTRODUCTION
The fracture of many materials in vacuum is accompanied by the emission of photons and particles. In particular, photon emission intensity is readily sampled on ns time scales and can provide a great deal of information concerning rapid (km/s) crack growth. In previous work, we showed that fluctuations in photon emission (phE) intensities during the fracture of a neat epoxy resin reflect variations in crack velocity and surface roughness.1 Further study indicated that these phE fluctuations are chaotic in nature, reflecting chaos in the process of rapid crack growth in this material.2 As pointed out by Goldberger, Rigney, and West,3 chaotic nonlinear dynamics often produce fractal structures, but the relations between the nonlinear dynamics and the resulting fractal structures are not easily established. These fractal structures include abstract elements of system dynamics such as the "path" of fracture in a suitable phase space (e.g., involving time and/or derivatives with respect to time) but also physical fractal objects, such as the resulting fracture surface. Empirical relations between fractal dimension measurements on fracture surfaces and material properties, such as fracture toughness, have been established for J. Mater. Res., Vol. 6, No. 1, Jan 1991 http://journals.cambr
Data Loading...
